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Proof step 108 from proof putarray-addarray-override (previous step)

0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0) ⊦ (putArray(vals, r0, i, addarray(r0, ty, vals0, st))[r0 -- i0 ']) = (addarray(r0, ty, firstn(i→n(i), vals0) + vals + restn(i→n(i) + # vals, vals0), st)[r0 -- i0 ']), ¬ i0 < 0 ∧ ¬ i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ≤ i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 67:
⊦ i < 0 ∨ n→i(# vals) ≤ i → (addarray(r, ty, vals, st)[r -- i ']) = st[r -- i ']
Proof step 107:
i0 < 0 ∨ n→i(# (firstn(i→n(i), vals0) + vals + restn(i→n(i) + # vals, vals0))) ≤ i0, 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0) ⊦ (putArray(vals, r0, i, addarray(r0, ty, vals0, st))[r0 -- i0 ']) = st[r0 -- i0 '], ¬ i0 < 0 ∧ ¬ i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ≤ i0

Rule argument

[crewrite-arg: add-at-other-index , F , [i, st, vals, ty, r] → [i0, st, firstn(i→n(i), vals0) + vals + restn(i→n(i) + # vals, vals0), ty, r0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ # (vals + vals0) = # vals + # vals0], [CSIMPSEQ : ⊦ # firstn(n, vals) = n], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ 0 ≤ i → n→i(i→n(i)) = i], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (i0, st, firstn(i→n(i), vals0) + vals + restn(i→n(i) + # vals, vals0), ty, r0)]]